For large deformations, you should use the Nonlinear Analysis option available in STAAD.Pro ( you will need the Advanced Analysis engine license ). Details on this type of analysis is available under the sections 1.18.2.3 and 5.37.8 of the Technical reference manual. You are correct that STAAD.Pro does not handle material nonlinearity. So any changes in stiffness due to change in the material strength has to be accounted for separately.
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